A 27-yard field goal by Zendejas with four seconds left lifted Washington to a 20-17 victory over the St. Louis Cardinals.
"It was a real struggle today," Washington Coach Joe Gibbs said. "It came down to one play, thank God we got it.
"It wasn't a letdown, we had too much on the line."
The victory improved the Redskins to 11-2 and clinched at least an NFC wild-card playoff spot.
"This is wonderful. It will give my teammates and my coaches confidence in me," Zendejas said. "I'm really comfortable now. I feel like I'm contributing."
Zendejas missed a 34-yarder earlier Sunday, but made up for it with his final kick.
"I thought we played good enough to win," said St. Louis Coach Gene Stallings of the defeat that left the Cardinals with a 3-10 record.
"We played hard. If we just make a play or two, we're in a position to win the game. But we didn't get the turnover we needed. That's been a problem all season."
St. Louis tied the game at 17-17 with 5:23 left on Neil Lomax's 35-yard pass to Roy Green, who made a fingertip grab in the right corner of the end zone.
Green hauled in the over-the-shoulder pass to beat Barry Wilburn.
"As far as I'm concerned, that was the catch of the year," Wilburn said. "I was all over him. He made some kind of catch."
Jay Schroeder's passes swept Washington to the winning points only after Cardinals linebacker Freddie Joe Nunn missed an interception on a deflected pass midway through the drive.
Schroeder completed 23 of 44 passes for 256 yards, with touchdown passes of 2 yards to Gary Clark and 22 yards to Terry Orr.
Lomax completed 10 of 16 passes for 159 yards for St. Louis, and Stump Mitchell rushed for 87 yards in 13 attempts.
St. Louis led 3-0 and 10-7 in the opening half, but the Redskins came back each time, moving ahead on Schroeder's pass to Orr and making it 17-10 at halftime on Zendejas' 30-yard field goal.
Eric Schubert kicked a 46-yard field goal for the Cards, and J.T. Smith caught a 4-yard pass from Lomax for St. Louis' second touchdown.